Landau and Kolmogoroff type polynomial inequalities
Contribuinte(s) |
Universidade Estadual Paulista (UNESP) |
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Data(s) |
20/05/2014
20/05/2014
01/01/1999
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Resumo |
Let 0<j<m less than or equal to n be integers. Denote by parallel to . parallel to the norm parallel to f parallel to(2) = integral(-infinity)(infinity) f(2)(x) exp(-x(2)) dx. For various positive values of A and B we establish Kolmogoroff type inequalitiesparallel to f((f))parallel to(2) less than or equal to A parallel to f(m)parallel to + B parallel to f parallel to/ A theta(k) + B mu(k),with certain constants theta(k)e mu(k), which hold for every f is an element of pi(n) (pi(n) denotes the space of real algebraic polynomials of degree not exceeding n).For the particular case j=1 and m=2, we provide a complete characterisation of the positive constants A and B, for which the corresponding Landau type polynomial inequalities parallel to f'parallel to less than or equal toA parallel to f parallel to + B parallel to f parallel to/ A theta(k) + B mu(k)hold. In each case we determine the corresponding extremal polynomials for which equalities are attained. |
Formato |
327-338 |
Identificador |
http://dx.doi.org/10.1155/S1025583499000430 Journal of Inequalities and Applications. Reading: Gordon Breach Sci Publ Ltd, v. 4, n. 4, p. 327-338, 1999. 1025-5834 http://hdl.handle.net/11449/21719 10.1155/S1025583499000430 WOS:000083720600004 WOS000083720600004.pdf |
Idioma(s) |
eng |
Publicador |
Gordon Breach Sci Publ Ltd |
Relação |
Journal of Inequalities and Applications |
Direitos |
openAccess |
Palavras-Chave | #Landau and Kolmogoroff type inequalities #Markov's inequality #hermite polynomials #extremal polynomials #Rayleigh-Ritz theorem |
Tipo |
info:eu-repo/semantics/article |